Worksheets - Week 6 - 1 Solving one-step equations Solutions PDF

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Worksheet 1 – One Step Equations (Addition or Subtraction) Solve the following equations for the missing variable. Show all steps using the balance method, as demonstrated below.

Example 𝑥 − 12 = 5 𝑥 − 12 + 𝟏𝟐 = 5 + 𝟏𝟐 𝑥 = 17

 Add 12 to both sides  Combine like terms

1) 𝑥 + 8 = 2

2) 𝑥 − 1 = −1

𝑥+8−𝟖=2−𝟖

𝑥 − 1 + 𝟏 = −1 + 𝟏

𝑥 = −6

𝑥=0

3) 𝑥 − 3 = 4

4) 𝑥 − 4 = 0

𝑥=7

𝑥=4

𝑥−3+𝟑=4+𝟑

𝑥−4+𝟒=0+𝟒

5) 𝑥 + 3 = −10

6) 𝑥 + 3 = −1

𝑥 + 3 − 𝟑 = −10 − 𝟑

𝑥 + 3 − 𝟑 = −1 − 𝟑

𝑥 = −13

𝑥 = −4

7) 2 + 𝑥 = −2

8) 10 + 𝑥 = −2

2 + 𝑥 − 𝟐 = −2 − 𝟐

10 + 𝑥 − 𝟏𝟎 = −2 − 𝟏𝟎

𝑥 = −4

𝑥 = −12

10) 𝑥 − (−2) = 5

9) −4 + 𝑥 = 6

−4 + 𝑥 + 𝟒 = 6 + 𝟒

𝑥+2=5

𝑥 = 10

𝑥+2−𝟐=5−𝟐 𝑥=3

[1]

12) 𝑥 + 12 = 2

Note: we still use the ”balance method” even though we don’t explicitly write it in the solutions as on the previous page.

𝑥 = 2 − 12

11) 𝑥 + 6 = 10

𝑥 = −10

𝑥 = 10 − 6 𝑥=4

13) 𝑥 − 5 = 11

14) 𝑥 − (−1) = −5

𝑥 = 16

𝑥 = −5 − 1

𝑥 = 11 + 5

𝑥 + 1 = −5 𝑥 = −6

15) −3 + 𝑥 = −2

16) −6 + 𝑥 = −4

𝑥 = −2 + 3

𝑥 = −4 + 6

𝑥=1

𝑥=2

17) −2 + 𝑥 = −4

18) −4 + 𝑥 = −5

𝑥 = −4 + 2

𝑥 = −5 + 4

𝑥 = −2

𝑥 = −1

19) 1 + 𝑥 = −9

20) 12 + 𝑥 = −4

𝑥 = −10

𝑥 = −16

𝑥 = −9 − 1

𝑥 = −4 − 12

21) 5 + 𝑥 = −2

22) 13 + 𝑥 = −6

𝑥 = −7

𝑥 = −19

𝑥 = −2 − 5

𝑥 = −6 − 13

[2]

Worksheet 2 – One Step Equations (Multiplication or Division) Solve the following equations for the missing variable. Show all steps using the balance method, as demonstrated below.

Example 1 −4𝑥 = −20 −4𝑥 −4

=

−20 −4

𝑥=5

 Divide both sides by -4 (since ‘x’ is being multiplied by -4)  Simplify

Example 2

𝑥

𝑥

−3

=6

−3 (−3) = −3(6) 𝑥 = −18

1)

𝑥 −2

 Multiply both sides by -3 (since ‘x’ is being divided by -3)  Simplify

2) 4𝑥 = −12

= −5

4𝑥 12 =− 𝟒 𝟒

𝑥 −𝟐 ( ) = −𝟐(−5) −2

𝑥 = −3

𝑥 = 10

3) 3.5𝑥 = 28

4)

3.5𝑥 28 = 𝟑. 𝟓 𝟑. 𝟓

𝑥 1.25

= −2

−𝟒 (

𝑥=8 5)

𝑥 −4

𝑥 ) = −𝟒(−2) −4

𝑥=8

6) 5𝑥 = 25

= −4

5𝑥 25 = 𝟓 𝟓

𝑥 𝟏. 𝟐𝟓 ( ) = 𝟏. 𝟐𝟓(−4) 1.25

𝑥=5

𝑥 = −5

[3]

7) −𝑥 = −2

8) −4𝑥 = −8

−𝑥

−2 = −𝟏 −𝟏

−

𝑥=2

9)

𝑥 −3

−8 = −𝟒 −𝟒

𝑥=2

= −1

−𝟑 (

4𝑥

10)

𝑥 ) = −𝟑(−1) −3

𝑥 −9

= −2

−𝟗 (

𝑥 ) = −𝟗(−2) −9

𝑥=3

𝑥 = 18

11) −𝑥 = −5 −𝑥 −5 = −𝟏 −𝟏

12) 2𝑥 = 18 2𝑥 18 = 𝟐 𝟐 𝑥=9

𝑥=5

13)

𝑥 −2

2 3

= −3

−𝟐 (

14) ( ) ∙ 𝑥 = 8

𝑥 ) = −𝟐(−3) −2

2 (3) 𝑥 𝟐 ( ) 𝟑

𝑥=6

=

𝑥 = 12

3 4

15) ( ) ∙ 𝑥 = 9

16)

3 ( )𝑥 9 4 = 𝟑 𝟑 (𝟒) ( ) 𝟒

𝑥

3

( ) 4

8 𝟐 (𝟑)

= 21

𝟑 𝟑 𝑥 ( ) = ( ) (21) 𝟒 (3) 𝟒 4 63 𝑥= 4 18) 9𝑥 = 18

𝑥 = 12

17) 0.5𝑥 = 12

0.5𝑥 12 = 𝟎. 𝟓 𝟎. 𝟓

9𝑥 18 = 𝟗 𝟗

𝑥 = 24

𝑥=2 [4]

Worksheet 3 – One Step Mixed Equations Solve the following equations for the missing variable.

1) 4𝑥 = 24 𝑥=

24 4

𝑥=6

4) −3𝑥 = −33 𝑥=

−33 −3

𝑥 = 11 7)

𝑥

= 12 4

𝑥 = 12(4) 𝑥 = 48

10) −12𝑥 = −24 𝑥=

−24 −12

𝑥=2

13) 𝑥 − 19 = 8 𝑥 = 8 + 19 𝑥 = 27

2) 𝑥 − 18 = 12

3)

𝑥 = 12 + 18

𝑥 = −3 − 4

𝑥=

−24 −2

𝑥 = 12

11) −𝑥 = 2 𝑥=

2 −1

𝑥 = −2

14) 8𝑥 = 56 𝑥=

56 8

𝑥=7

[5]

=8

𝑥 = 56

6) 𝑥 − 12 = −1 𝑥 = −1 + 12

𝑥 = −7

8) −2𝑥 = −24

7

𝑥 = 8(7)

𝑥 = 30

5) 𝑥 + 4 = −3

𝑥

𝑥 = 11

9)

𝑥

−3

= −8

𝑥 = −8(−3) 𝑥 = 24

12) 2 + 𝑥 = 9 𝑥 =9−2 𝑥=7

𝑥

15) 0.5 = 28

𝑥 = 28(0.5) 𝑥 = 14

16) −5𝑥 = −25 𝑥=

−25 −5

𝑥=5

2

19) 𝑥 − = 4 3

2 𝑥 =4+ 3 14 𝑥= 3

22) −𝑥 = 12 12 𝑥= −1

𝑥 = −12

𝑥

25) 0.5 = −18

𝑥 = −18(0.5) 𝑥 = −9

17)

𝑥

= −1 −4

𝑥 = −1(−4) 𝑥=4

1

18) 𝑥 = 3 2 𝑥=

3 1 (2)

𝑥=6 20) −2𝑥 = −8 𝑥=

−8 −2

𝑥=4 1

23) 3 𝑥 =

1

9

1 (9) 𝑥= 1 (3) 1 𝑥= 3

26) 2.5𝑥 = −12.5 𝑥=

−12.5 2.5

𝑥 = −5

[6]

21) −18𝑥 = −36 𝑥=

−36 −18

𝑥=2 2

24) 𝑥 = 3

5

7

5 ( ) 𝑥= 7 2 (3) 15 𝑥= 14...